Question

What is the least number of students in a class if they can be made to stand in rows of 8, 12 or 14 each?

• A. 248
• B. 224
• C. 196
• D. 168
• E. 242

Answer 1

The Correct Option is D

Step 1: Understand the problem.
We need to find the least number of students in a class such that they can be arranged in rows of 8, 12, or 14 students each. This means we need to find the least common multiple (LCM) of 8, 12, and 14.

Step 2: Find the prime factorization of the numbers.
The prime factorization of each number is:
- 8 = \( 2^3 \)
- 12 = \( 2^2 \times 3 \)
- 14 = \( 2 \times 7 \)

Step 3: Find the LCM of the numbers.
To find the LCM, we take the highest power of each prime factor that appears in the factorizations:
- The highest power of 2 is \( 2^3 \)
- The highest power of 3 is \( 3^1 \)
- The highest power of 7 is \( 7^1 \)
Therefore, the LCM is:
LCM = \( 2^3 \times 3 \times 7 = 8 \times 3 \times 7 = 168 \)

Step 4: Conclusion.
The least number of students that can be arranged in rows of 8, 12, or 14 students is 168.

Final Answer:
The correct option is (D): 168.